Can you find two vectors with different lengths that have a vector sum of zero? What length restrictions are required for three vectors to have a vector sum zero? Explain.

Answer 1

If F1 + F2 = 0, They must be equal in magnitude and opposite in direction. They cannot have different magnitudes(lengths).

If F1 and F2 are unequal, a third force may be added to give a sum of zero. However, the third force must be equal to the sum of the first two and opposite in direction:

F1+F2 + F3 = 0, F3 = -(F1+F2) = -F1-F2.

Remember, we are talking about VECTOR sums.